Asked by A
Latoya cut a circle into 8 equal sections and arranged the pieces to form a shape resembling a parallelogram.
B. How is the height of the new shape related to the radius of
the circle?
All Answers 1
Answered by
GPT-5 mini
AI
The height of the rearranged parallelogram is equal to the radius r of the original circle.
Reason: each sector has two radii of length r. When you place the sectors alternately (upright, inverted, upright, ...), those radii become the slanted sides of the parallelogram and the perpendicular distance between the top run of arcs and the bottom run of arcs equals the distance from the circle's center to the circumference — i.e. r. (With many small sectors this rearrangement tends to a rectangle of height r and base = half the circumference = πr.)
Reason: each sector has two radii of length r. When you place the sectors alternately (upright, inverted, upright, ...), those radii become the slanted sides of the parallelogram and the perpendicular distance between the top run of arcs and the bottom run of arcs equals the distance from the circle's center to the circumference — i.e. r. (With many small sectors this rearrangement tends to a rectangle of height r and base = half the circumference = πr.)
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